The filtered Poincaré lemma in higher level (with applications to algebraic groups)

Details The filtered Poincaré lemma in higher level (with applications to algebraic groups) The filtered Poincaré lemma in higher level (with applications to algebraic groups)

2004-09-29

arxiv.org/abs/math/0409564v1

Mathematics

Algebraic Geometry

Latex, 25 pages

Scientific paper

We show that the Poincar\'e lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincar\'e lemma for transversal crystals of level m. We interpret the de Rham complex in terms of what we call the Berthelot-Lieberman construction, and show how the same construction can be used to study the conormal complex and invariant differential forms of higher level for a group scheme. Bringing together both instances of the construction, we show that crystalline extensions of transversal crystals by algebraic groups can be computed by reduction to the filtered de Rham complexes. Our theory does not ignore torsion and, unlike in the classical (m=0), not all closed forms are invariant. Therefore, close invariant differential forms of level m provide new invariants and we exhibit some examples as applications.

Affiliated with

Also associated with

No associations

Rating

The filtered Poincaré lemma in higher level (with applications to algebraic groups) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The filtered Poincaré lemma in higher level (with applications to algebraic groups), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The filtered Poincaré lemma in higher level (with applications to algebraic groups) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-23832